The Initial Mass Function (IMF) is a crucial concept in astrophysics that describes the distribution of masses for a population of stars when they form. It provides a statistical representation of how many stars are born within a certain mass range in a stellar population, essentially outlining the relationship between the number of stars and their masses at the time of formation.
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The initial mass function specifies the distribution of stellar masses at birth. Writing means that counts the expected number born in a small mass interval. Counts per logarithmic interval differ: . Confusing these conventions changes the reported slope even for the same population.
For a chosen finite birth-mass range, gives the number of stars and their total mass. The mass and luminosity weighting of a stellar initial mass function explains why a small number of luminous massive stars can dominate the light without dominating the count. A present-day distribution also reflects deaths, continued star formation, unresolved companions and observational selection, so it is not automatically the birth distribution.